2. ©1999 by Design Science, Inc. Pre-Calculus Lesson 2: Algebra of Functions

3. ©1999 by Design Science, Inc. 2 Basic function operations  Sum  Difference  Product  Quotient x x

4. ©1999 by Design Science, Inc. 3 Composition of functions  Composition of functions is the successive application of the functions in a specific order.  Given two functions f and g, the composite function is defined by and is read “f of g of x.”

5. ©1999 by Design Science, Inc. 4 A different way to look at it… Function Machine x Function Machine g f

6.  Evaluate and :  ©1999 by Design Science, Inc. 5 Example

7.  Evaluate and :  ©1999 by Design Science, Inc. 6 Example

8.  Evaluate and :  ©1999 by Design Science, Inc. 7 Example

9.  Evaluate and :  ©1999 by Design Science, Inc. 8 Example You can see that function composition is not commutative!

10. ©1999 by Design Science, Inc. 9 THE DIFFERENCE QUOTIENT

11. ©1999 by Design Science, Inc. 10 THE DIFFERENCE QUOTIENT

12. ©1999 by Design Science, Inc. 11 Example: Given f(x)=3x-7, find

13. ©1999 by Design Science, Inc. 12 Example: Given f(x)=3x-7, find

14. ©1999 by Design Science, Inc. 13 Example: Given f(x)=3x-7, find

15. ©1999 by Design Science, Inc. 14 Example: Given f(x)=3x-7, find

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22. ©1999 by Design Science, Inc. 21 Example: f(x) = 3x 2 - 4x - 5 http://www.pstcc.edu/facstaff/jahrens/math1730/worksheets/diffquot.pdf

23. ©1999 by Design Science, Inc. 22 Example: f(x) = 3x 2 - 4x - 5 http://www.pstcc.edu/facstaff/jahrens/math1730/worksheets/diffquot.pdf

24. ©1999 by Design Science, Inc. 23 Example: f(x) = 3x 2 - 4x - 5 http://www.pstcc.edu/facstaff/jahrens/math1730/worksheets/diffquot.pdf

25. ©1999 by Design Science, Inc. 24 Example: f(x) = 3x 2 - 4x - 5 http://www.pstcc.edu/facstaff/jahrens/math1730/worksheets/diffquot.pdf

26. ©1999 by Design Science, Inc. 25 Example: f(x) = 3x 2 - 4x - 5 http://www.pstcc.edu/facstaff/jahrens/math1730/worksheets/diffquot.pdf

27. ©1999 by Design Science, Inc. 26 Example: f(x) = 3x 2 - 4x - 5 http://www.pstcc.edu/facstaff/jahrens/math1730/worksheets/diffquot.pdf

28. ©1999 by Design Science, Inc. 27 Example: f(x) = 3x 2 - 4x - 5 http://www.pstcc.edu/facstaff/jahrens/math1730/worksheets/diffquot.pdf

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33. Practice: For the function f(x)=2x 2 + 3, find: a)f(2) b)f(t) c)f(x+h) d) ©1999 by Design Science, Inc. 32